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Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing

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  • Andrew Hunt
  • David Blake

Abstract

Many users of mortality models are interested in using them to place values on longevity-linked liabilities and securities. Modern regulatory regimes require that the values of liabilities and reserves are consistent with market prices (if available), though the gradual emergence of a traded market in longevity risk needs methods for pricing new types of longevity-linked securities quickly and efficiently. In this study, we develop a new forward mortality framework to enable the efficient pricing of longevity-linked liabilities and securities in a market-consistent fashion. This approach starts from the historical data of the observed mortality rates, i.e., the force of mortality. Building on the dynamics of age/period/cohort models of the observed force of mortality, we develop models of forward mortality rates and then use a change of measure to incorporate whatever market information is available. The resulting forward mortality rates are then used to value a number of different longevity-linked securities, such as q-forwards, s-forwards, and longevity swaps.

Suggested Citation

  • Andrew Hunt & David Blake, 2021. "Forward Mortality Rates in Discrete Time I: Calibration and Securities Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(S1), pages 482-507, February.
    • Handle: RePEc:taf:uaajxx:v:25:y:2021:i:s1:p:s482-s507
    DOI: 10.1080/10920277.2019.1649159
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Miguel Santolino, 2023. "Should Selection of the Optimum Stochastic Mortality Model Be Based on the Original or the Logarithmic Scale of the Mortality Rate?," Risks, MDPI, vol. 11(10), pages 1-21, September.

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